IEEE Computational Intelligence Magazine - May 2022 - 74

Assuming that the optimal classifier
obtained on the current AUCE task is
wE, the training instances used by the
AUCC task are dynamically adjusted
according to the performance of all data
on the classifier wE. First, calculate all the
instances' output values in the whole
dataset on the classifier wE. Then assign a
Algorithm 2 Framework of EMTAUC.
Input:
S: the whole dataset used in AUCE;
s: the sampling rate;
d: the generation interval for dynamic
adjusting strategy;
m: the penalty parameter;
p: the parameter of the MTO algorithm;
Output:
w*: the optimal parameter of model f.
1. F1, F2!Initiate the AUCC and AUCE task
according to (6);
2. P1, P2!Perform the Initialization
module in an MTO algorithm (such as
MFEAII, SBO, or EMEA);
3. t!1;
4. while (stopping criterion is not met) do
5.
6.
if mod(, )t d 0= then
7.
F1!Perform the dynamic adjustment
strategy of AUCC (Algorithm 1);
Re-evaluate P1 on task F1;
8. end if
9. P1, P2!Perform the Main Loop
module in an MTO algorithm (such
as MFEAII, SBO, or EMEA);
10. tt 1! + ;
11. end while
12. w*!Obtain the optimal parameter of
model f from P2.
score to each instance to select those
instances that are not easily identifiable
by the classifier wE. The score of each
positive instance is the number of negative
instances whose output value is
greater than or equal to the output value
of the positive instance. Similarly, the
score of each negative instance is the
number of positive instances whose output
value is less than the output value of
the negative example. The greater the
score of an instance, the more difficult it
is to identify this instance. Therefore, the
instances with high scores are employed
to adjust the training data used by the
AUCC task to make full use of the
knowledge contained in these instances.
C. Framework of EMTAUC
The framework of EMTAUC is shown
in Algorithm 2. As can be observed,
AUCC and AUCE tasks are initialized to
build a multitasking AUC optimization
environment. Then the two tasks are
optimized simultaneously through any
general EMTO algorithm such as
MFEAII, SBO, and EMEA, where effective
knowledge transfer between AUCC
and AUCE tasks can speed up the convergence
of expensive tasks. In addition,
to ensure the diversity of knowledge
transfer, the sampling dataset of AUCC
tasks is dynamically adjusted after a cerTABLE
II Dataset statistics.
#ID
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:
15:
DATASET
DIABETES
FOURCLASS
GERMAN
SPLICE
USPS
AUSTRALIAN
A9A
SONAR
SVMGUIDE1
SVMGUIDE3
SEGMENT
IJCNN1
SATIMAGE
VOWEL
POKER
tain number of generations (d generations).
According to the outputs of all
samples on the optimal classifier
obtained by the current AUCE task, the
instances that are more difficult to identify
are added to the AUCC tasks (see
Algorithm 1). In this method, the maximum
computational cost is the stopping
criterion. The computational cost of a
function evaluation of an AUCC task is
considered as 1, and that of a function
evaluation of an AUCE task is regarded
as 1/s2.
VI. Experiments
A. Experimental Setup
1) Datasets. In this paper, EMTAUC is
evaluated on 15 datasets, including diabetes,
fourclass, german, splice, usps, australian,
a9a, sonar, svmguide1, svmguide3,
segment, ijcnn1, satimage, vowel, and
poker from the LIBSVM website [5].
These datasets are widely studied binary
classification datasets. These datasets are
commonly used for AUC optimization, as
shown in many works [1]-[9]. The features
for all datasets have been scaled to [-1, 1],
and the multi-class dataset is randomly
divided into two groups, each of which
contains the same number of classes. For
each dataset, the number of negative and
positive instances is shown in Table II,
together with dimensionality d.
2) Algorithm. MFEAII [28], SBGA
T+ + T−
768
862
1000
1000
7291
690
32561
208
3089
1243
2310
49990
4435
528
25010
T+
500
307
300
517
2596
307
7841
97
2000
296
990
4853
1189
240
23221
T−
268
555
700
483
4695
383
24720
111
1089
947
1320
45137
3246
288
1789
d
8
2
24
60
256
14
123
60
4
22
19
22
36
10
10
[27], EMEA [26], and SBCMAES [27],
four state-of-the-art EMTO algorithms,
are embedded in EMTAUC as the MTO
optimizer to form EMTAUC-MFEAII,
EMTAUC-SBGA, EMTAUC-EMEA,
and EMTAUC-SBCMAES, respectively.
In addition to the above EA-based
methods, the nine state-of-the-art
MOEAs or online AUC approaches are
considered as baselines to demonstrate
the effectiveness of EMTAUC in the
experiments, which are ETriCM [16],
MKnEA-AUC [20], OAMseq, OAMinf,
OAMgra [21], Perceptron [22], CPA [23],
CW [24], and PA [23]. ETriCM and
MKnEA-AUC are representative methods
based on convex hull and multi-level
knee point, respectively, so they are
selected as the compared algorithms.
Moreover, two basic single-task solvers,
74 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2022
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